Question

please answer this question

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Answer 1

Answer:

hope this helps u..........

Answer 2

Solution :

Let us assume that,

• p(x) = 2x³ + ax² + 3x - 5

• g(x) = x³ + x² - 4x + a

Now,

By Using remainder theorem :

if f(x) is divided by (x - a) then the remainder is f(a).

______________________......

$\dag \: \: \sf p(x) = g(x) \: \: \: \: \tiny \bigg \lgroup \bf{ \because \: p(x) \: and \: g(x) \: both \: divided \: by \: (x - 2) \: and \: both \: remainder \: are \: same \bigg \rgroup}$

$\bigstar \: \sf \: 2x^{3} + ax^{2} + 3x - 5 = x ^{3} + x^{2} - 4x + a \: \bigstar$

$\star\:\sf 2(2)^{3} + a(2)^{2} + 3(2) - 5 = (2) ^{3} + {(2)}^{2} - 4(2) + a\:\star$

$: \implies \sf 16 + 4a + 6 - 5 = \cancel{8} + 4 - \cancel{8} + a$

$: \implies \sf 17 - 4 = - 3a$

$: \implies \sf 13 = - 3a$

$: \implies \underline {\boxed{\sf a = \dfrac{ - 13}{3}} }$

$\underline{\therefore \textsf {The \: value \: of \: a \: is \: \: \textbf{-13/3}}}$